(a) Field of the Invention
The present invention relates to an iterative decoding receiver in a spatial multiplexing system and a method thereof. More particularly, the present invention relates to an iterative decoding receiver for reducing complexity of a partial sphere decoding operation in a spatial multiplexing system, and reducing complexity of a soft input soft output (SISO) sphere decoding operation in the iterative decoding receiver using Bahl-Cocke-Jelinek-Raviv (BCJR), message passing algorithm (MPA), and Viterbi algorithm (VA) decoding algorithms in a channel encoding multiple antenna system, and a method thereof.
(b) Description of the Related Art
It is required to detect a maximum likelihood (ML) to obtain a maximized performance in a coded multiple input multiple output (MIMO) system. However, as the number of antennas is increased, complexity of an optimum receiving method by detecting the ML is exponentially increased. Accordingly, to solve a problem of the complexity of the ML detection, a V-BLAST-based soft iterative decoding method for obtaining a quasi-optimum solution by performing nulling-cancellation has been actively studied. However, the performance of quasi-optimum detection-based soft iterative decoding methods including zero forcing (ZF) and minimum mean square error (MIMSE) equalization is deteriorated, compared to ML detection-based methods.
Various efforts have been made to reduce the complexity of the ML in the MIMO system. Among the efforts, a sphere decoding method has been actively studied (E. Viterbo and J. Boutrous, “A universal lattice code decoder for fading channels,” IEEE Trans. Inform. Theory, vol 45, pp 1639-1642, July 1997). The sphere decoding method has been introduced in a Fincke-Posht algorithm, and it has been reintroduced in an uncoded system by Viterbi.
When the sphere decoding method is applied to a multiple antenna system, the complexity of the maximum likelihood is considerably reduced, but the problem of the complexity still remains. Accordingly, various studies have been performed to reduce the complexity of the sphere decoding algorithm, which reduces the complexity of the sphere decoding algorithm so that the sphere decoding algorithm may be actually realized. However, the studies for the sphere decoding algorithm have been proceeded to reduce the complexity and complement the algorithm under the uncoded MIMO environment. Vikalo has suggested a modified sphere decoding algorithm for performing soft iterative decoding by using a soft input soft output (SISO) in the coded MIMO system, which has drawn attention to the sphere decoding algorithm used when an iterative decoding process using a soft value is performed.
In an iterative decoding method according to the turbo principle by using decoding algorithms including a message passing algorithm (MPA) and a Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm based on the modified sphere decoding algorithm by Vikalo (Vikalo, H, Hassibi, B and Kailath “Iterative decoding for MIMO channels via modified sphere decoding, “T.; Wireless Communications, IEEE Transactions on Volume 3, Issue 6, Nov. 2004 Page(s): 2299-2311), a coding gain that is close to an optimum value is obtained in respective channel convolutional codes (e.g., Convolution code, turbo code, LDPC).
However, the complexity caused when soft values for respective encoded bits are provided to a channel decoder in a SISO sphere decoding process may become a considerable problem as the number of antennas is increased.
As the prior art, in an iterative maximum a posterior (MAP) receiver having low complexity based on the sphere decoding (Seung Young Park, Soo Ki Choi, and Chung Gu Kang, “Complexity-Reduced Iterative MAP Receiver for Spatial Multiplexing Systems,” IEE Proceedings of Communications, August 2004), the complexity is reduced since the sphere decoding algorithm is not applied to bits having a high reliability based on an extrinsic probability output from a MAP decoder. Even though the complexity of the SISO sphere decoding algorithm is reduced according to the prior art, the complexity still remains.
The iterative MAP receiver reduces the complexity caused by the optimum detection since the iterative MAP receiver partially performs the MAP detection under an assumption that an a priori probability of a transmission symbol has been informed.
In addition, a transaction entitled “On the Partial MAP detection with Applications to MIMO Channels,” in IEEE Transaction on signal processing, Vol 53, No. 1, January 2005 by Jinho Choi, introduced a partial MAP rule having a performance that is similar to the performance obtained when an overall MAP detection is performed. The partial MAP rule is given as Equation 1. s2=arg max Pr(s2), r2=r−H2 s2  [Equation 1]
 s2 denotes a set of sub-transmission symbols having a maximum a priori probability for a set s2 of sub-transmission symbols.
                                          min                          s              1                                ⁢                                    1                              N                0                                      ⁢                                                                                                r                    2                                    -                                                            H                      1                                        ⁢                                          s                      1                                                                                                  2                                      ≤                  C          +                                    min                                                s                  2                                ≠                                  s                  _                                                      ⁢                          log              ⁢                                                Pr                  ⁡                                      (                                                                  s                        _                                            2                                        )                                                                    Pr                  ⁡                                      (                                          s                      2                                        )                                                                                                          [                  Equation          ⁢                                          ⁢          2                ]            
C denotes a Euclidean distance between a receipt vector and a set of subcarrier symbols estimated to have a second highest a priori probability next to s2.
N denotes a noise variance.
                                          s            _                    1                =                              min                          s              1                                ⁢                                    1                              N                0                                      ⁢                                                                                                r                    2                                    -                                                            H                      1                                        ⁢                                          s                      1                                                                                                  2                                                          [                  Equation          ⁢                                          ⁢          3                ]            
In Equations 1, 2, and 3, s1 and s2 denote sets of sub-transmission symbol vectors of transmission symbols s. r1 and r2 denote sub-receipt symbols. H1 and H2 denote sub-channel matrixes of an overall channel matrix.
When Equation 2 is satisfied, the optimum detection performance for all the symbols may be achieved only by performing the optimum detection for s1 (here, s1 denotes a set of sub-transmission symbol vectors minimizing an Euclidean distance to a sub-receipt symbol vector r2 of the sub-transmission symbol set s1) in Equation 3.
Equations 4, 5, 6, and 7 respectively show a cost function-based partial MAP rule for preventing a performance degradation of the partial MAP when the a priori probability of the estimated transmission symbols is less than a reference value and there is no dominant sub-transmission symbol.
Equation 4 shows a cost function relating to the sub-transmission symbol set s1.
Pr(s2) denotes an a priori probability of the sub-transmission symbol set s2.
                              C          ⁡                      (                          s              1                        )                          =                              E                          s              2                                ⁡                      [                                                            1                                      N                    0                                                  ⁢                                                                                                r                      -                                                                        H                          1                                                ⁢                                                  s                          1                                                                    -                                                                        H                          2                                                ⁢                                                  s                          2                                                                                                                          2                                            +                              log                ⁢                                  1                                      Pr                    ⁡                                          (                                              s                        1                                            )                                                                                            ]                                              [                  Equation          ⁢                                          ⁢          4                ]            
Equation 5 defines an average sub-symbol vector for the sub-transmission symbol set s2 when there is no dominant a priori probability.
                                          s            ~                    2                =                              ∑                          s              2                                ⁢                                    s              2                        ⁢                          Pr              ⁡                              (                                  s                  2                                )                                                                        [                  Equation          ⁢                                          ⁢          5                ]            
Equation 6 shows a process for finding {tilde over (s)}app,1 which is an approximated s1 for minimizing a cost function for the sub-transmission symbol set s1.
                                                                        s                ~                                            app                ⁢                                  ,                  1                                                      =                                                                                arg                    ⁢                                                                                  ⁢                    min                                                        s                    1                                                  ⁢                                  C                  ⁡                                      (                                          s                      1                                        )                                                              =                                                                    arg                    ⁢                                                                                  ⁢                    min                                                        s                    1                                                  ⁢                                  1                                      N                    0                                                  ⁢                                                                                                                        r                        2                                            -                                                                        H                          1                                                ⁢                                                  s                          1                                                                                                                          2                                                              ,                                          ⁢          here                ⁢                                  ⁢                              r            2                    =                      r            -                                          H                2                            ⁢                                                s                  ~                                2                                                                        [                  Equation          ⁢                                          ⁢          6                ]            
A cost function for the sub-transmission symbol set s2 is given as Equation 7.
                              C          ⁡                      (                          s              2                        )                          =                              E                          s              1                                ⁡                      [                                                            1                                      N                    0                                                  ⁢                                                                                                r                      -                                                                        H                          1                                                ⁢                                                  s                          1                                                                    -                                                                        H                          2                                                ⁢                                                  s                          2                                                                                                                          2                                            +                              log                ⁢                                  1                                      Pr                    ⁡                                          (                                              s                        2                                            )                                                                                            ]                                              [                  Equation          ⁢                                          ⁢          7                ]            
Equation 8 shows an average symbol vector of the {tilde over (s)}app,1 calculated in Equation 6.
                                          s            ~                    1                =                              ∑                          s              1                                ⁢                                                    s                ~                                            app                ⁢                                  ,                  1                                                      ⁢                          Pr              ⁡                              (                                                      s                    ~                                                        app                    ⁢                                          ,                      1                                                                      )                                                                        [                  Equation          ⁢                                          ⁢          8                ]            
In Equation 9, {tilde over (s)}app,2, an approximated s2 for minimizing a cost function for the sub-transmission symbol vector set s2, is calculated.
When there is no dominant a priori probability, the iterative MAP receiver calculates the average symbol vector and the received sub-symbol vector by using the a priori probability of a corresponding sub-symbol vector and symbols in the cost function, and applies the partial MAP rule.
                                                                        s                ~                                            app                ⁢                                  ,                  2                                                      =                                                                                arg                    ⁢                                                                                  ⁢                    min                                                        s                    2                                                  ⁢                                  C                  ⁡                                      (                                          s                      2                                        )                                                              =                                                                    arg                    ⁢                                                                                  ⁢                    min                                                        s                    2                                                  ⁢                                  1                                      N                    0                                                  ⁢                                                                                                                        r                        1                                            -                                                                        H                          2                                                ⁢                                                  s                          2                                                                                                                          2                                                              ,                                          ⁢          here                ⁢                                  ⁢                              r            1                    =                      r            -                                          H                1                            ⁢                                                s                  ~                                1                                                                        [                  Equation          ⁢                                          ⁢          9                ]            
In the partial MAP rule according to the prior art, it is assumed that the a priori probability is detected in an early detection process, but it is assumed, in an actual system, that the a priori probabilities for the respective transmission symbols are the same.
Accordingly, in a channel encoding MIMO system, the conventional partial MAP rule may not be applied in the early detection process. In addition, in the multiple antenna system, when the partial MAP using the partial MAP rule is detected, the calculating complexity is problematically increased as the number of antennas and modulation exponents are increased.
There is a problem in realizing the channel encoding MIMO system since the ML/sphere decoding operation based on the optimum detection has the considerable complexity as the number of antennas and modulation exponents is increased when the iterative decoding for the optimum performance is performed. In addition, the SISO sphere decoding based on the optimum detection has the considerable complexity as the number of antennas and modulation exponents are increased in the multiple antenna system.
The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.